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Calculus for Team-Based Inquiry Learning: 2024 Edition PREVIEW

TBIL Institute Fellows

Section 5.7 Integration strategy (TI7)

Subsection 5.7.1 Activities

Activity 5.7.1.

Consider the integral \(\displaystyle\int e^t \tan(e^t) \sec^2(e^t)\,dt\text{.}\) Which strategy is a reasonable first step to make progress towards evaluating this integral?
  1. The method of substitution
  2. The method of integration by parts
  3. Trigonometric substitution
  4. Using a table of integrals
  5. The method of partial fractions

Activity 5.7.2.

Consider the integral \(\displaystyle\int \frac{2x+3}{1+x^2}\,dx\text{.}\) Which strategy is a reasonable first step to make progress towards evaluating this integral?
  1. The method of substitution
  2. The method of integration by parts
  3. Trigonometric substitution
  4. Using a table of integrals
  5. The method of partial fractions

Activity 5.7.3.

Consider the integral \(\displaystyle\int \frac{x}{\sqrt[3]{1-x^2}}\,dx\text{.}\) Which strategy is a reasonable first step to make progress towards evaluating this integral?
  1. The method of substitution
  2. The method of integration by parts
  3. Trigonometric substitution
  4. Using a table of integrals
  5. The method of partial fractions

Activity 5.7.4.

Consider the integral \(\displaystyle\int \frac{1}{2x\sqrt{1-36x^2}}\,dx\text{.}\) Which strategy is a reasonable first step to make progress towards evaluating this integral?
  1. The method of substitution
  2. The method of integration by parts
  3. Trigonometric substitution
  4. Using a table of integrals
  5. The method of partial fractions

Activity 5.7.5.

Consider the integral \(\displaystyle\int t^5\cos(t^3)\,dt\text{.}\) Which strategy is a reasonable first step to make progress towards evaluating this integral?
  1. The method of substitution
  2. The method of integration by parts
  3. Trigonometric substitution
  4. Using a table of integrals
  5. The method of partial fractions

Activity 5.7.6.

Consider the integral \(\displaystyle\int \frac{1}{1+e^x}\,dx\text{.}\) Which strategy is a reasonable first step to make progress towards evaluating this integral?
  1. The method of substitution
  2. The method of integration by parts
  3. Trigonometric substitution
  4. Using a table of integrals
  5. The method of partial fractions

Subsection 5.7.2 Videos

Figure 111. Video: I can select appropriate strategies for integration
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